Consecutive Integers and Equations

The video tutorial covers writing equations using symbols, translating verbal statements into mathematical equations, and solving problems involving consecutive integers. It provides examples and practice problems to help students understand the process of converting words into equations and solving them.

Why is it often easier to understand mathematical expressions than word problems?

• Expressions are always in English.

• Expressions use symbols that are universally understood.

• Expressions are more colorful.

• Expressions are shorter.

What does the phrase 'half the number is added to 15' translate to in an equation?

• 15x = 0.5

• x - 15 = 0.5x

• 0.5x + 15 = x

• x + 15 = 0

In the equation '5x - 0.5x^2 = x', what operation is performed first?

• Multiplication

• Division

• Addition

• Subtraction

If Paulo spends $6 and has a fourth of his original amount left, what equation represents this situation?

• x - 6 = 0.25x

• x + 6 = 0.25x

• x - 6 = 4x

• x + 6 = 4x

What does the equation '57 - x = 5x + 4' represent?

• A number is added to 57.

• A number is divided by 57.

• 57 is multiplied by a number.

• A number is subtracted from 57 and the result is 4 more than five times the number.

How do you set up an equation for the sum of three consecutive integers?

• x + x + 1 + x + 2 = 372

• x + x + 2 + x + 4 = 372

• x + x + 3 + x + 6 = 372

• x + x + 1 + x + 3 = 372

What is the first step in solving the equation for three consecutive integers that sum to 93?

• Multiply both sides by 3

• Divide both sides by 3

• Add 3 to both sides

• Subtract 3 from both sides

What is the value of x if the sum of three consecutive integers is 93?

• 32

• 30

• 31

• 33

What is the next step after setting up the equation for consecutive integers?

• Solve for x

• Add all integers

• Subtract integers

• Multiply integers

What is the sum of the integers 30, 31, and 32?

• 90

• 91

• 93

• 92